Lost the only key, PATS system is there a way to get my system working without having any of the original transponder keys?

While camping in a remote area I lost my only key for my truck listed above, not realizing I had the PATS System I broke out the key cylinder to try and start it with a screwdriver. I've looked into using a bypass module but I'm leery about the chance of doing more damage. I am pretty sure that I did not damage anything but the key cylinder. I am able to completely remove the key cylinder. If I purchased a new cylinder with programmable keys. Is there a way to get my system working without having any of the original transponder keys?